Discussion
The ratio of two numbers a and b is 3:7. After adding 9 to each number, the ratio becomes 9:17. The numbers a and b are
Answer: D
The numbers are (18, 42).
Let a = 3k and b = 7k. After adding 9 to each:
\[ \begin{aligned} \frac{3k + 9}{7k + 9} &= \frac{9}{17} \\ 51k + 153 &= 63k + 81 \\ 12k &= 72, \quad k = 6 \end{aligned} \]
So a = 18 and b = 42. Check: 27/51 = 9/17. (9, 21) and (15, 35) are also in the ratio 3:7 but give 18/30 and 24/44, and (8, 42) is not in the ratio 3:7 at all.
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